Since the '90s for me.
I was introduced to him in B:TAS and then when I started reading the comics I liked him being around (and even getting the occasional spotlight). Bruce having a non-Bat family friend and trusted advisor who was just a decent man that handled Bruce's company is a breath of fresh air and helps make the world feel real. Lucius was a great side character and that was all he needed to be.
Not everybody in a hero's world needs to be an active part (or even know of) of their costumed life.
That said, I like that Jace is a retooled Timothy Fox and it actually does make sense for the character to end up here.